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{f(x)=x3+ax2+bx+cg(x)=x3+bx2+cx+a\begin{cases} f(x)={ x }^{ 3 }+{ a }x^{ 2 }+bx+c \\ g(x)={ x }^{ 3 }+{ b }x^{ 2 }+cx+a \end{cases}{f(x)=x3+ax2+bx+cg(x)=x3+bx2+cx+a Given that a,b,ca, b, ca,b,c are integers with c≠0c\neq 0c=0 and the following conditions hold for the above functions:
(a) f(1)=0f(1) = 0f(1)=0;
(b) the roots of g(x)=0g(x) = 0g(x)=0 are the squares of the roots of f(x)=0f(x) = 0f(x)=0.
Find the absolute value of (a2013+b2013+c2013).({ a }^{ 2013 }+{ b }^{ 2013 }+{ c }^{ 2013 }).(a2013+b2013+c2013).
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